// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_SOLVE_H
#define EIGEN_SOLVE_H

namespace Eigen {

template <typename Decomposition, typename RhsType, typename StorageKind> class SolveImpl;

/** \class Solve
  * \ingroup Core_Module
  *
  * \brief Pseudo expression representing a solving operation
  *
  * \tparam Decomposition the type of the matrix or decomposition object
  * \tparam Rhstype the type of the right-hand side
  *
  * This class represents an expression of A.solve(B)
  * and most of the time this is the only way it is used.
  *
  */
namespace internal {

    // this solve_traits class permits to determine the evaluation type with respect to storage kind (Dense vs Sparse)
    template <typename Decomposition, typename RhsType, typename StorageKind> struct solve_traits;

    template <typename Decomposition, typename RhsType> struct solve_traits<Decomposition, RhsType, Dense>
    {
        typedef typename make_proper_matrix_type<typename RhsType::Scalar,
                                                 Decomposition::ColsAtCompileTime,
                                                 RhsType::ColsAtCompileTime,
                                                 RhsType::PlainObject::Options,
                                                 Decomposition::MaxColsAtCompileTime,
                                                 RhsType::MaxColsAtCompileTime>::type PlainObject;
    };

    template <typename Decomposition, typename RhsType>
    struct traits<Solve<Decomposition, RhsType>>
        : traits<typename solve_traits<Decomposition, RhsType, typename internal::traits<RhsType>::StorageKind>::PlainObject>
    {
        typedef typename solve_traits<Decomposition, RhsType, typename internal::traits<RhsType>::StorageKind>::PlainObject PlainObject;
        typedef typename promote_index_type<typename Decomposition::StorageIndex, typename RhsType::StorageIndex>::type StorageIndex;
        typedef traits<PlainObject> BaseTraits;
        enum
        {
            Flags = BaseTraits::Flags & RowMajorBit,
            CoeffReadCost = HugeCost
        };
    };

}  // namespace internal

template <typename Decomposition, typename RhsType> class Solve : public SolveImpl<Decomposition, RhsType, typename internal::traits<RhsType>::StorageKind>
{
public:
    typedef typename internal::traits<Solve>::PlainObject PlainObject;
    typedef typename internal::traits<Solve>::StorageIndex StorageIndex;

    Solve(const Decomposition& dec, const RhsType& rhs) : m_dec(dec), m_rhs(rhs) {}

    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_dec.cols(); }
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }

    EIGEN_DEVICE_FUNC const Decomposition& dec() const { return m_dec; }
    EIGEN_DEVICE_FUNC const RhsType& rhs() const { return m_rhs; }

protected:
    const Decomposition& m_dec;
    const RhsType& m_rhs;
};

// Specialization of the Solve expression for dense results
template <typename Decomposition, typename RhsType> class SolveImpl<Decomposition, RhsType, Dense> : public MatrixBase<Solve<Decomposition, RhsType>>
{
    typedef Solve<Decomposition, RhsType> Derived;

public:
    typedef MatrixBase<Solve<Decomposition, RhsType>> Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)

private:
    Scalar coeff(Index row, Index col) const;
    Scalar coeff(Index i) const;
};

// Generic API dispatcher
template <typename Decomposition, typename RhsType, typename StorageKind>
class SolveImpl : public internal::generic_xpr_base<Solve<Decomposition, RhsType>, MatrixXpr, StorageKind>::type
{
public:
    typedef typename internal::generic_xpr_base<Solve<Decomposition, RhsType>, MatrixXpr, StorageKind>::type Base;
};

namespace internal {

    // Evaluator of Solve -> eval into a temporary
    template <typename Decomposition, typename RhsType>
    struct evaluator<Solve<Decomposition, RhsType>> : public evaluator<typename Solve<Decomposition, RhsType>::PlainObject>
    {
        typedef Solve<Decomposition, RhsType> SolveType;
        typedef typename SolveType::PlainObject PlainObject;
        typedef evaluator<PlainObject> Base;

        enum
        {
            Flags = Base::Flags | EvalBeforeNestingBit
        };

        EIGEN_DEVICE_FUNC explicit evaluator(const SolveType& solve) : m_result(solve.rows(), solve.cols())
        {
            ::new (static_cast<Base*>(this)) Base(m_result);
            solve.dec()._solve_impl(solve.rhs(), m_result);
        }

    protected:
        PlainObject m_result;
    };

    // Specialization for "dst = dec.solve(rhs)"
    // NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere
    template <typename DstXprType, typename DecType, typename RhsType, typename Scalar>
    struct Assignment<DstXprType, Solve<DecType, RhsType>, internal::assign_op<Scalar, Scalar>, Dense2Dense>
    {
        typedef Solve<DecType, RhsType> SrcXprType;
        static void run(DstXprType& dst, const SrcXprType& src, const internal::assign_op<Scalar, Scalar>&)
        {
            Index dstRows = src.rows();
            Index dstCols = src.cols();
            if ((dst.rows() != dstRows) || (dst.cols() != dstCols))
                dst.resize(dstRows, dstCols);

            src.dec()._solve_impl(src.rhs(), dst);
        }
    };

    // Specialization for "dst = dec.transpose().solve(rhs)"
    template <typename DstXprType, typename DecType, typename RhsType, typename Scalar>
    struct Assignment<DstXprType, Solve<Transpose<const DecType>, RhsType>, internal::assign_op<Scalar, Scalar>, Dense2Dense>
    {
        typedef Solve<Transpose<const DecType>, RhsType> SrcXprType;
        static void run(DstXprType& dst, const SrcXprType& src, const internal::assign_op<Scalar, Scalar>&)
        {
            Index dstRows = src.rows();
            Index dstCols = src.cols();
            if ((dst.rows() != dstRows) || (dst.cols() != dstCols))
                dst.resize(dstRows, dstCols);

            src.dec().nestedExpression().template _solve_impl_transposed<false>(src.rhs(), dst);
        }
    };

    // Specialization for "dst = dec.adjoint().solve(rhs)"
    template <typename DstXprType, typename DecType, typename RhsType, typename Scalar>
    struct Assignment<DstXprType,
                      Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType>>, RhsType>,
                      internal::assign_op<Scalar, Scalar>,
                      Dense2Dense>
    {
        typedef Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType>>, RhsType> SrcXprType;
        static void run(DstXprType& dst, const SrcXprType& src, const internal::assign_op<Scalar, Scalar>&)
        {
            Index dstRows = src.rows();
            Index dstCols = src.cols();
            if ((dst.rows() != dstRows) || (dst.cols() != dstCols))
                dst.resize(dstRows, dstCols);

            src.dec().nestedExpression().nestedExpression().template _solve_impl_transposed<true>(src.rhs(), dst);
        }
    };

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_SOLVE_H
